LEETCODE 498 : FLIP DIRECTION PATTERN: Diagonal Traverse - Efficient Solution and Walkthrough"

Welcome to our comprehensive walkthrough of LeetCode Problem 498: Diagonal Traverse. In this video, we will dive deep into understanding the problem, explore efficient solutions, and provide you with step-by-step guidance to solve it effectively.
Introduction
Diagonal Traverse is a classic problem that tests your ability to traverse a matrix in a diagonal order. It is essential to understand how to manipulate matrix indices and manage the traversal direction to solve this problem efficiently. In this video, we will cover everything from the problem statement to the solution, ensuring you have a solid grasp of the concepts involved.
Problem Statement
The problem requires you to return all the elements of a given matrix in a diagonal order. The matrix is represented as a two-dimensional array, and you need to start the traversal from the top-left corner, moving diagonally towards the bottom-right corner.
Key Points to Consider
Matrix Dimensions: Understand the dimensions of the matrix. The number of rows and columns will impact how you traverse the matrix diagonally.
Traversal Directions: Diagonal traversal can be tricky because it involves alternating directions. Starting from the top-left, the direction changes at each step.
Edge Cases: Consider edge cases such as single-row or single-column matrices. These cases require special handling to ensure the traversal is correct.
Approach and Strategy
To solve this problem efficiently, we need a clear strategy to traverse the matrix diagonally. Here’s a step-by-step approach:
Initialization:
Start from the top-left corner of the matrix.
Initialize variables to keep track of the current row and column.
Use a flag to indicate the current direction of traversal.
Traversal:
Use a loop to iterate through the elements of the matrix.
Depending on the current direction, update the row and column indices.
If moving upwards (diagonal right), decrement the row index and increment the column index.
If moving downwards (diagonal left), increment the row index and decrement the column index.
Direction Change:
Change the traversal direction when you reach the boundary of the matrix.
Handle the cases where you reach the last row or column to avoid out-of-bound errors.
Edge Handling:
Ensure that edge cases are handled correctly. For instance, if the matrix has only one row or one column, the traversal should be straightforward without changing directions.
Detailed Explanation
Let’s break down the solution with a detailed explanation of each step:
Step 1: Initialization
Start by initializing the following variables:
row and col to track the current position in the matrix.
direction to track the current direction of traversal (upwards or downwards).
Step 2: Traversal
Use a loop to traverse the matrix:
If the current direction is upwards:
Decrement the row index.
Increment the column index.
If the current direction is downwards:
Increment the row index.
Decrement the column index.
Step 3: Direction Change
When you reach the boundary of the matrix:
If you are moving upwards and reach the top row or the last column, change the direction to downwards.
If you are moving downwards and reach the bottom row or the first column, change the direction to upwards.
Step 4: Edge Handling
Handle special cases:
If the matrix has only one row, the traversal should move horizontally across the columns.
If the matrix has only one column, the traversal should move vertically across the rows.
Example Walkthrough
Let’s walk through an example to understand the traversal process:
Consider the matrix:
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[
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
The diagonal traversal would be: [1, 2, 4, 7, 5, 3, 6, 8, 9]
Iteration 1:
Start at (0, 0): Add 1 to the result.
Move to (0, 1): Add 2 to the result.
Iteration 2:
Change direction to downwards.
Move to (1, 0): Add 4 to the result.
Move to (2, 0): Add 7 to the result.
Iteration 3:
Change direction to upwards.
Move to (1, 1): Add 5 to the result.
Move to (0, 2): Add 3 to the result.
Iteration 4:
Change direction to downwards.
Move to (1, 2): Add 6 to the result.
Move to (2, 1): Add 8 to the result.
Iteration 5:
Change direction to upwards.
Move to (2, 2): Add 9 to the result.
Conclusion
Diagonal Traverse is a fascinating problem that helps improve your understanding of matrix manipulations and traversal techniques. By following a structured approach and handling edge cases, you can solve this problem efficiently.
Tips for Efficient Coding
Plan Your Approach: Before jumping into coding, take some time to plan your approach. Visualize the matrix and how you will traverse it diagonally.
Handle Edge Cases: Always consider edge cases. Think about scenarios where the matrix has minimal dimensions and how your solution will handle them.

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